Mathematics questions
18011 published questions with worked solutions.
- Choose the correct statement about two circles whose equations are given below : x^2+y^2-10x-10y+41=0 and x^2+y^2-22x-10y+137=0
- Let , , be the real roots of the equation, x^3+ax^2+bx+c=0, (a,b,c R and a,b 0). If the system of equations (in, u, v, w) given...
- The integral (2x-1 ) 2x-1^2+5 4x^2-4x+6 dx is equal to (where c is a constant of integration)
- The equation of one of the straight lines which passes through the point (1,3) and makes an angle ^ -1 ( 2) with the straight...
- If _ x 0 ^ -1 x- ^ -1 x 3x^3 is equal to L, then the value of (6L + 1) is equal to :
- A vector a has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle...
- If the equation a|z|^2+ z+ z+d=0 represents a circle where a,d are real constants, then which of the following condition is...
- For the four circles M, N, O and P, following four equations are given : Circle M : x^2+y^2=1 Circle N : x^2+y^2-2x=0 Circle O :...
- If , are natural numbers such that 100 -99 =(100)(100)+(99)(101)+(98)(102)+ +(1)(199), then the slope of the line passing through...
- The real valued function f(x)= cosec ^ -1 x x-[x] , where [x] denotes the greatest integer less than or equal to x, is defined...
- If the functions are defined as f(x) = x and g(x) = 1-x , then what is the common domain of the following functions : f+g, f–g,...
- If f(x)= cases 1 |x| , & |x| 1 ^2+b, & |x|<1 cases is differentiable at every point of the domain, then the values of a and b are...
- Let A+2B= bmatrix 1&2&0 6&-3&3 -5&3&1 bmatrix And 2A-B= bmatrix 2&-1&5 2&-1&6 0&1&2 bmatrix . If Tr(A) denotes the sum of all...
- The sum of all the 4-digit distinct numbers that can be formed with the digits 1,2,2 and 3 is :
- The number of times the digit 3 will be written when listing the integers from 1 to 1000 is
- Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, –3, 1) and (2, 3, –5) at the right angles. If a, b, c,...
- Let f(x) and g(x) be two functions satisfying f(x^2)+g(4-x)=4x^3 and g(4-x)+g(x)=0, then the value of _ -4 ^4f(x)^2dx is
- Let z_1, z_2 be the roots of the equation z^2+az+12=0 and z_1,z_2 form an equilateral triangle with origin. Then, the value of...
- The equation of the planes parallel to the plane x – 2y + 2z – 3 = 0 which are at unit distance from the point (1, 2, 3) are ax +...
- The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in...